04 Aug 2023
 | 04 Aug 2023

Numerical coupling of aerosol emissions, dry removal, and turbulent mixing in the E3SM Atmosphere Model version 1 (EAMv1), part II: a semi-discrete error analysis framework for assessing coupling schemes

Christopher J. Vogl, Hui Wan, Carol S. Woodward, and Quan M. Bui

Abstract. Part I of this study discusses the motivation and empirical evaluation of a revision to the aerosol-related numerical process coupling in the atmosphere component of the Energy Exascale Earth System Model version 1 (EAMv1) to address the previously reported issue of strong sensitivity of the simulated dust aerosol lifetime and dry removal rate to the model's vertical resolution. This paper complements that empirical justification of the revised scheme with a mathematical justification leveraging a semi-discrete analysis framework for assessing the splitting error of process coupling methods. The framework isolates the error due to numerical splitting from the error from the time integration method(s) used for each individual process. The result is a splitting error expression that is more easily interpreted in the context of the physical processes that the terms represent. The application of this framework to dust life cycle in EAMv1 showcases such an interpretation, using the leading-order splitting error that results from the framework to confirm (i) that the original EAMv1 scheme artificially strengthens the effect of dry removal processes, and (ii) that the revised splitting reduces that artificial strengthening.

While the error analysis framework is presented in the context of the dust life cycle in EAMv1, the framework can be broadly leveraged to evaluate process coupling schemes, both in other physical problems and for any number of processes. This framework will be particularly powerful when the various process implementations support a variety of time integration approaches. Whereas traditional local truncation error approaches require separate consideration of each combination of time integration methods, this framework enables evaluation of coupling schemes independent of particular time integration approaches for each process while still allowing for the incorporation of these specific time integration errors if so desired. The framework also explains how the splitting error terms result from (i) the integration of individual processes in isolation from other processes and (ii) the choices of input state and timestep size for the isolated integration of processes. Such a perspective has the potential for rapid development of alternative coupling approaches that utilize knowledge both about the desired accuracy and about the computational costs of individual processes.

Christopher J. Vogl et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on egusphere-2023-1356', Anonymous Referee #1, 02 Sep 2023
  • RC2: 'Comment on egusphere-2023-1356', Anonymous Referee #2, 15 Sep 2023

Christopher J. Vogl et al.

Data sets

EAMv1 output from simulations using tag v1_cflx_2021: annual averages Hui Wan, Kai Zhang

EAMv1 output from simulations using tag v1_cflx_2021: instantaneous values Hui Wan, Kai Zhang

Model code and software

EAMv1 code with revised aerosol process coupling (tag v1_cflx_2021) Hui Wan

Christopher J. Vogl et al.


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Short summary
Generally speaking, accurate climate simulation requires an accurate evolution of the underlying mathematical equations on large computers. The equations are typically formulated and evolved in process groups. Process coupling refers to how the evolution of those groups of combined to evolve the full set of equations for the whole atmosphere. This work presents a mathematical framework to evaluate methods without the need to first implement the methods.